Developments in the Academy from the time of Arcesilaus to that of Carneades and his successors tend to be classified under two heads: scepticism and probabilism. Carneades was principally responsible for the Academy's view of the latter subject, and our sources credit him with an elaborate discussion of it. The evidence furnished by those sources is, however, frequently confusing and sometimes self-contradictory. My aim in this paper is to extract a coherent account of Carneades' theory of probability from the testimony with a further end in view, namely to understand better the uses to which that theory was put by the Academy in its debate with the Stoa. Though it is not its principal object, the investigation should also help make clear how the Academy's scepticism and its probabilism were related to each other as parts of a single consistent practice of philosophy